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SUBROUTINE ZGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, M, N
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* .. Array Arguments ..
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DOUBLE PRECISION D( * ), E( * )
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COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * )
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* ZGEBD2 reduces a complex general m by n matrix A to upper or lower
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* real bidiagonal form B by a unitary transformation: Q' * A * P = B.
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* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
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* The number of rows in the matrix A. M >= 0.
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* The number of columns in the matrix A. N >= 0.
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* A (input/output) COMPLEX*16 array, dimension (LDA,N)
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* On entry, the m by n general matrix to be reduced.
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* if m >= n, the diagonal and the first superdiagonal are
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* overwritten with the upper bidiagonal matrix B; the
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* elements below the diagonal, with the array TAUQ, represent
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* the unitary matrix Q as a product of elementary
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* reflectors, and the elements above the first superdiagonal,
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* with the array TAUP, represent the unitary matrix P as
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* a product of elementary reflectors;
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* if m < n, the diagonal and the first subdiagonal are
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* overwritten with the lower bidiagonal matrix B; the
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* elements below the first subdiagonal, with the array TAUQ,
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* represent the unitary matrix Q as a product of
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* elementary reflectors, and the elements above the diagonal,
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* with the array TAUP, represent the unitary matrix P as
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* a product of elementary reflectors.
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* See Further Details.
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* The leading dimension of the array A. LDA >= max(1,M).
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* D (output) DOUBLE PRECISION array, dimension (min(M,N))
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* The diagonal elements of the bidiagonal matrix B:
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* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1)
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* The off-diagonal elements of the bidiagonal matrix B:
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* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
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* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
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* TAUQ (output) COMPLEX*16 array dimension (min(M,N))
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* The scalar factors of the elementary reflectors which
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* represent the unitary matrix Q. See Further Details.
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* TAUP (output) COMPLEX*16 array, dimension (min(M,N))
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* The scalar factors of the elementary reflectors which
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* represent the unitary matrix P. See Further Details.
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* WORK (workspace) COMPLEX*16 array, dimension (max(M,N))
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value.
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* The matrices Q and P are represented as products of elementary
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* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1)
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* Each H(i) and G(i) has the form:
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* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
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* where tauq and taup are complex scalars, and v and u are complex
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* vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
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* A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
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* A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
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* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m)
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* Each H(i) and G(i) has the form:
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* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'
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* where tauq and taup are complex scalars, v and u are complex vectors;
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* v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
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* u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
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* tauq is stored in TAUQ(i) and taup in TAUP(i).
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* The contents of A on exit are illustrated by the following examples:
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* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n):
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* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 )
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* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 )
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* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 )
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* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 )
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* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 )
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* where d and e denote diagonal and off-diagonal elements of B, vi
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* denotes an element of the vector defining H(i), and ui an element of
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* the vector defining G(i).
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* =====================================================================
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PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
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$ ONE = ( 1.0D+0, 0.0D+0 ) )
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* .. Local Scalars ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZLACGV, ZLARF, ZLARFG
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG, MAX, MIN
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* .. Executable Statements ..
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* Test the input parameters
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ELSE IF( N.LT.0 ) THEN
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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CALL XERBLA( 'ZGEBD2', -INFO )
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* Reduce to upper bidiagonal form
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* Generate elementary reflector H(i) to annihilate A(i+1:m,i)
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CALL ZLARFG( M-I+1, ALPHA, A( MIN( I+1, M ), I ), 1,
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* Apply H(i)' to A(i:m,i+1:n) from the left
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$ CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
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$ DCONJG( TAUQ( I ) ), A( I, I+1 ), LDA, WORK )
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* Generate elementary reflector G(i) to annihilate
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CALL ZLACGV( N-I, A( I, I+1 ), LDA )
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CALL ZLARFG( N-I, ALPHA, A( I, MIN( I+2, N ) ), LDA,
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* Apply G(i) to A(i+1:m,i+1:n) from the right
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CALL ZLARF( 'Right', M-I, N-I, A( I, I+1 ), LDA,
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$ TAUP( I ), A( I+1, I+1 ), LDA, WORK )
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CALL ZLACGV( N-I, A( I, I+1 ), LDA )
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* Reduce to lower bidiagonal form
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* Generate elementary reflector G(i) to annihilate A(i,i+1:n)
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CALL ZLACGV( N-I+1, A( I, I ), LDA )
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CALL ZLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA,
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* Apply G(i) to A(i+1:m,i:n) from the right
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$ CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
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$ TAUP( I ), A( I+1, I ), LDA, WORK )
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CALL ZLACGV( N-I+1, A( I, I ), LDA )
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* Generate elementary reflector H(i) to annihilate
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CALL ZLARFG( M-I, ALPHA, A( MIN( I+2, M ), I ), 1,
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* Apply H(i)' to A(i+1:m,i+1:n) from the left
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CALL ZLARF( 'Left', M-I, N-I, A( I+1, I ), 1,
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$ DCONJG( TAUQ( I ) ), A( I+1, I+1 ), LDA,
added
removed
libcruft/lapack/zgebd2.f
